A Primer of Nonlinear Analysis

A Primer of Nonlinear Analysis

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This is an introduction to nonlinear functional analysis, in particular to those methods based on differential calculus in Banach spaces. It is in two parts; the first deals with the geometry of Banach spaces and includes a discussion of local and global inversion theorems for differentiable mappings. In the second part, the authors are more concerned with bifurcation theory, including the Hopf bifurcation. They include plenty of motivational and illustrative applications, which indeed provide much of the justification of nonlinear analysis. In particular, they discuss bifurcation problems arising from such areas as mechanics and fluid dynamics. The book is intended to accompany upper division courses for students of pure and applied mathematics and physics; exercises are consequently included.show more

Product details

  • Online resource
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • 36 b/w illus.
  • 1139172204
  • 9781139172202

Review quote

'There's no more economical or lucid introduction to the subject than this great little book.' The Mathematical Intelligencershow more

Table of contents

Preface; Preliminaries and notation; 1. Differential calculus; 2. Local inversion theorems; 3. Global inversion theorems; 4. Semilinear Dirichlet problems; 5. Bifurcation results; 6. Bifurcation problems; 7. Bifurcation of periodic solutions; Further reading.show more